University of Cambridge > > Category Theory Seminar > Betweenness reals: How to do Dedekind cuts when you don't know which way is up

Betweenness reals: How to do Dedekind cuts when you don't know which way is up

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If you have a question about this talk, please contact Tamara von Glehn.

Recently Vaughan Pratt claimed on the categories list that any of the standard constructions of the reals from the rationals could be carried out using only the affine-space structure of the rationals. As I pointed out at the time, that is not quite true, because the Dedekind-cuts construction makes essential use of the order-relation on Q, which is not definable from the affine structure since Q has order-reversing affine automorphisms. However, Q does have a ternary ‘betweenness’ relation definable from its affine structure. In this talk I shall investigate how the Dedekind-cuts construction can be made to work for spaces equipped with a betweenness structure: the results are mostly predictable, but there are one or two unexpected twists.

This talk is part of the Category Theory Seminar series.

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